Tools Application Rules · PDF fileKey skills of BB : Process knowledge, Good observation and correct selection of tools 1 Six Sigma Implementation Tools Application Rules Checklist

Key skills of BB : Process knowledge, Good observation and correct selection of tools 1

Six Sigma ImplementationTools Application Rules Checklist

20th June2007


Six Sigma ImplementationTools Application Rules Index

18th July 2007 Ver: 1

68-72M&AVariable Search – Process OptimizationDOE#9

35-36M&AModified Component Search – Attribute responseDOE#4

33-34M&AModified Component Search – Variable responseDOE#4

Define

Define

Control

M&A

M&A

Improve

M&A

M&A

M&A

M&A

M&A

M&A

DMAIC Phases

89-90Instrument CalibrationDOE#12

84-86R&R StudyDOE#11

77-80Variation analysisDOE#10

74Full FactorialDOE#9

62-66Variable Search – Problem solving DOE#8

57B vs CDOE#7

54Concentration chartDOE#6

45Multi vari analysisDOE#5

29-30Component Search – Attribute responseDOE#3

27-28Component Search – Variable responseDOE#3

24Product/Process SearchDOE #2

20-21Paired ComparisonDOE #1

SlidesTechnique DescriptionTool No.


SIX SIGMA

•• 3 Sigma Level3 Sigma Level------------------ Tolerance= 6Tolerance= 6σσ

Defect Rate= 2700ppmDefect Rate= 2700ppm

•• 6 Sigma Level6 Sigma Level------------------ 50% of Tolerance= 650% of Tolerance= 6σσ

Defect Rate= 3ppbDefect Rate= 3ppb


• Key to the success of Six Sigma:

• Process knowledge

• Knowledge in selection and application of DOE tools

• Top Management Commitment

• Strong Review Mechanism

• Six Sigma was first developed by: Mr Bill Smith, Motorola, 1986

• Six Sigma Improvement Process structure adopted: DMAIC

• Funneling for identification of cause is done till it is found that cause is controllable.

• Cause which is controllable is the root cause of the problem.

• Six Sigma is all about reducing & eliminating wastes in all processes.

• Methodology adopted for six Sigma is Funneling.

• Objective of Six Sigma is to improve RTY and operate all processes at “Six Sigma level”.

• Objective of Six Sigma is to operate all measurable outcome of the processes at “Six Sigma level” and attribute outcomes of the processes at “Zero Defect.”

• Key to achieving Six Sigma Level is “ Process knowledge, correct selection and application of DOE Tool and innovative solutions in improving the process”

• Six sigma is the estimated Part to Part variation at 99.73% CL

Six sigma – General understanding


Selection of Six sigma Projects

Problem Solving Process Optimization

Critical to Quality (CTQ)

Critical to Cost

(CTC)

Critical to Satisfaction

(CTS)


How to select Problem solving BB projects

Cause known

Solution Known

Cause known

Solution Unknown

Cause Unknown

Solution Unknown

Cause Unknown

Solution known

CauseKnown Unknown

Solution

Know

nU

nknown

Six sigma project – Priority # 1

Six sigma project – Priority # 2

1

2 4

3

Types of Problems Six sigma project – Priority # 3

Always check the Basic machine condition for any obvious abnormalities and correct it before selecting the project. Select it as a project only if the problem persists after

ensuring basic machine condition


ProcessVariation

Input MaterialVariation

Poor ProcessDesign

Poor ProductDesign

Machine

Tooling ParameterVariation

MethodVariation

ProcessingMaterial

Environment

Source of Variations


DMAIC ProcessDefine theProblem

Measure &Analysis

Improve

Control

- Provide full information about the problem such as the rejection %, Suspected sources of variations for the problem, type of response

Apply DOE techniques and arrive at the “Root cause”(Controllable cause) for the problem

Validate the Root cause using B vs C

Identify and Implement solution for eliminating the root causes

Identify and Implement control measures for the root cause to make sure that the problem is prevented from occurring again


Define the ProblemStart

Is problemknown? Problem Statement

Select one Product/Assembly

Is RTY100%?

Use RTY Technique

Map the Process

Calculate RTY

Type ofResponse

Note Specification

List instrumentsUsed

LC≤10% of tolerance

Is R&RRequired?

Do Study

List out 1st levelSuspected Source of Variation( SSV’s)SSVs only related to

Input material Variation. Name of the process will be

listed as SSV

X

Variable

Attribute

No

No

No

Yes

Yes

Yes

Note:R&R study is needed only when there is chance of error in measurement due to man.


Suspected Source of Variation (SSVs)To start with List down only First Level source of variation

•Last Process in which the response is generated

•Do not brainstorm and list down the detailed sources of variations within the process

•Input Material Parameters which can technically create the problem

Do not list down SSV related to Process and Product design. ( SSV which can not vary during process)

- Some examples are Speed of spindle, Feed Rate, Time, Injection pressure, Limit switch position


M&A phase: Selection of Tools for SSV

DOE Tools Situation/ Condition

T1Paired Comparison

•When SSV can bemeasured on Good and Bad Products/Parts/Components•Process parameter whosedata is available for Good/Bad•Response can be eitherattribute or Variable•M&A Phase

T2Process/ Product

Search

•When SSV can not bemeasured on Good andBad Products//Parts•Response can be eitherattribute or Variable•M&A Phase



T3Component search

•When problem is on an assembledproduct & the assembly can bedis-assembled and re-assembledwithout damaging parts

•Response can be eitherattribute or Variable•M&A Phase

T4Modified

Component search

•When problem is on an assembledproduct & if some parts get damaged during disassembly

•Response can be eitherattribute or Variable•M&A Phase




T5Multi VariAnalysis

When input material is not the Cause of the problem and processIs the only cause of the problemResponse has to be Variable•M&A Phase

T6Concentration

charts

•When the problem can come atany location on the product and we have to study the defect pattern•Response can be eitherattribute or Variable•M&A Phase




T7B Vs C

When root cause of the problem Or optimal setting for a process is identified and it has to validatedImprovement Phase

T8Variable Search

When the problem is due to design parameters of Product/ Process & parameters are >3Process to be optimized for >3 design parametersM&A Phase



Selection of Tools for SSVDOE Tools Situation/ Condition

T9Full Factorial

When the problem is due to design parameters of Product/ Process & parameters are ≤ 3Process to be optimized for <=3Design parametersM&A Phase

T10Variation Analysis

When the action on root cause is implemented and type of control to be decided for monitoring.This can be done both for Root X as well as Big YControl Phase


Selection of Tools for SSVDOE Tools Situation/ Condition

T11R&R study

When the measurement variation can come due to method of checking and we have to find out the variation due to the personwho is checkingDefine phase

T12Calibration

When the variation can come due to Instrument and we have to find outthe variation of the instrument onlyDefine phase


Steps after selection of Tools for SSV during M&A Phase

1. Data Collection ( Minimum data collection without affecting the production processes)

2. Analysis (Simple analysis without using calculators and big jargons so that anybody can do it)

3. Conclusion (Accurate conclusion on the cause(s))

Root Cause Identification


DOE Tool 1

Paired Comparison


Application:• Is used when SSV is measurable on both good and bad products

• Good & Bad are selected based on the response defined in the problem definition

• Response can be Variable or attribute

• SSV can be Variable or attribute

• Is applicable to input material related SSV or to the process parameter variation provided the historic data is available withtraceability

M&A Phase DOE 1 –Paired Comparison


If the Variation is >75% of the New tolerance, then the Confirmed cause is only a “CAUSE”and this should be taken as Y and drilled down further

If the Variation is <=75% of the New tolerance, then the Confirmed cause is a “ROOT CAUSE”

Calculate the variation as the maximum –minimum of all the 12 or 16 data

Remember !! – The BOB and WOW are selected based on the Response

For geometrical parameters, Do not do fine tuning, Fix only USL based on the data, since the LSL is always zero

If the Problem statement is “Parameter variation”, select the BOB as the product with less variation from target and WOW as the product with maximum variation from the target value

Fine tune the specification by adding or subtracting the existing tolerance depending on where the GOOD band is located

If the SSV is attribute, scale on a scale of 0-3, 0 –SSV not present 1- SSV present with less severity, 2-SSV present with medium severity, 3- SSV present with high severity and record the data

For all the causes with Count >=6, fix the specification based on the “GOOD” band

Measure the SSV’s on the Good and Bad products and record the data if the SSV is variable

If we have to prioritize the causes with Total count >=6, then apply Variable Search or Full factorial tool

If the rejection percentage is <=0.5%, select 6 BOB and 6 WOW instead of 8 BOB and 8 WOW

We cannot prioritize causes with Total count >=6, based on the Count value.

If the response is attribute and WOW selection is not possible, select 8 Good and 8 Bad

For one problem, we can have more than one SSV with counts >=6. In this case, all are the confirmed causes

If the maximum and minimum value belong to different category, do the counting as per the flow diagram given in the next slide

Select 8 Good and 8 WOW if the response is “attribute”

If the Total count is >=6, then the SSV is the confirmed cause for the problem

If the maximum and minimum value belong to the same category, then the cause is eliminated and the Total count is 0

Select 8 BOB and 8 WOW if the response is “variable”

ConclusionAnalysisData Collection

M&A Phase: DOE1- Paired Comparison rules Checklist


Flow diagram for finding total count

Does the minimum value and the maximum value belong to the same category

Arrange values in ascending order

From the top, check for the first time a transition is happening and draw the line and similarly from the bottom at the first transition, draw the line

Are the value repeating at the transition line

Does the repeated values belong to the same category

How many repetitions are there ??

Is the arrangement correct, if not rearrange (follow step 4)

Count and reduce 0.5

Do analysis as per Step # 5

Count is “0”and this is not the reason for problem

Do normal counting as per Step # 3

NoYes

Yes

Yes

No

No

Only 2

> 2

M&A Phase: DOE1- Paired Comparison


DOE Tool 2

Product/Process Search


Application:• When the sources of variation is not measurable on both

Good and Bad Products/Parts

• SSV related to process parameter or product characteristics that can not be measured on Good and Bad parts.

• Is used when SSV are process/ machine parameters like Temperature, Pressure, pouring time, etc.

• related to input material dimensions, but the dimensions will get changed during processing preventing the application of paired comparison.

• Response can be Variable or attribute. SSV’s can be attribute or variable

M&A Phase DOE 2 –Product/Process Search


If Method #2 data collection is done and 8 or 6 bad are not obtained and the response is attribute, then we have to collect more data till we get 6 or 8 Bad

If Method #2 data collection is done and 8 or 6 bad is not obtained in the lot, then check the following condition if the response is variable-Find out the variation of the entire data-If the variation is >=80% of tolerance, further data collection is not required-If the variation is <80% of tolerance, then collect for one more lot and again check the variation of both the data. Do like this till variation is >=80% of tolerance

Decide the lot size for Method # 2 data collection based on the historic rejection.Eg: if the historic rejection is 8%, decide the lot size as 100 pcs

If any one of the above conditions are not satisfied, then follow Method # 2 data collection

-Rejection % is > 1%-Input material SSV’ s can be checked near the machine-Inspection cycle time of the SSV’s are less than the Process cycle time of one part-Response can be checked/measured near the machine-Response can be checked/measured immediately after the process is completed

Same rules as Paired comparisonSame rules as Paired ComparisonFollow Method # 1 data collection when the following conditions are satisfied


M&A Phase: DOE2- Product/Process search rules checklist


DOE Tool 3

Component Search


Application:• When the problem is on an assembled product & assembly can be

disassembled and reassembled without damaging the parts

• Is used for assembly related problems ( HV Failure, Leakage, Vibration, Pressure Drop, etc.)


M&A Phase DOE 3 – Component Search


M&A Phase: DOE3- Component Search rules checklist

Variable response

Stage # 1Stage # 1Stage #1

If the conclusion is component is the reason for the problem, the go to Stage # 2

If the conclusion is Assembly process is the reason for the problem, use Multivari analysis as the next tool

Totally, we will have 3 data for Good assembly and 3 data for Bad assembly

D/d ratio <1.25, then Assembly Process is the reason for the problem

Disassemble and Reassemble WOW assembly two times and record the data. Use the same components

D/d ratio >=1.25 and <3 and there is “Overlap”between the 3 data of Good and 3 data of Bad, then Assembly Process is the reason for the problem

Disassemble and Reassemble BOB assembly two times and record the data. Use the same components

D/d ratio >=1.25 and <3 and there is “No overlap” between the 3 data of Good and 3 data of Bad, then Components are the reasons for the problem and Assembly process is not the reason for the problem

When calculating d value, the number of decimal places should be one decimal more than in the data

Note down the data as selected

D/d ratio >=3, Components are the reasons for the problem and Assembly process is not the reason for the problem

D = Difference of the Mediand = Average of Ranges

Take one BOB and one WOW assembly




Variable response

Same rules as Paired comparisonSame rules as Paired compairsonSelect 8 BOB and 8 WOW assemblies. Remove the parts pinpointed earlier as per step 2 and then check the suspected dimensions on those parts

Only one line crossing the middle line. Conclusion: One of the component creating the problem

For A+R- data, use the Bad assembly legend“-” indicates Bad assembly and “+” indicates Good assembly


Stage # 3 – Paired comparisonStage # 3 – Paired ComparisonStage # 3 – Paired Comparison

If A is “one of the components” and B is “the only component”, Do paired comparison only on B

Do the conclusion as per the conclusion rules and then decide to interchange the next component

Stop the swapping, when the conclusion comes as the Only component creating the problem

A+R- means – Component A taken from Good assembly and put inside Bad assembly

If we get, A as one of the components, B as one of the components creating the problem, we should not go for C, we have to interchange A&B together

Decision line (Middle line) is Average of MediansA-R+ means – Component A taken from Bad assembly and put inside Good assembly

No line crosses the middle line: Component not at all creating the problem

For A-R+ data, use the good assembly legendSwap the first component. The swapping is represented as A-R+ and A+R-

Both lines crossing the middle line (Average of median line). Conclusion: Only component creating problem

When plotting the data, represent bad assembly data as “dotted line” and Good assembly data as “Sold line”

List down the Components in the descending order of suspect level




Attribute response


If Assembly process is the reason for the problem, then we have investigate by “Observing the assembly process”

If Components are the reason for the problem go to Stage #2

No data will be measured and recorded. Just record the status of the assembly as “Good” and “Bad”

Good assembly becomes bad or Bad assembly becomes good, then Assembly process is the reason for the problem

Dissemble and Reassemble Good assembly two time and Bad assembly two times. Use the same components

Good assembly remains Good and Bad assembly remains Bad, Components are the reasons for the problem and Assembly process is not the reason for the problem

No calculations are doneTake one Good and one Bad assembly




Attribute response

Same rules as Paired comparisonSame rules as Paired compairsonSelect 8 Good and 8 Bad assemblies. Remove the parts pinpointed earlier as per step 2 and then check the suspected dimensions on those parts

If Good assembly remains Good and Bad assembly remains Bad, then the Component interchanged is “Not at all” the reason for the problem

“-” indicates Bad assembly and “+” indicates Good assembly



Stage # 3 – Paired ComparisonStage # 3 – Paired Comparison





If Good assembly remains Good and Bad assembly becomes Good, then the Component interchanged is “One of the component”creating the problem

A-R+ means – Component A taken from Bad assembly and put inside Good assembly

If Good assembly becomes Bad and Bad assembly remains Bad, then the Component interchanged is “One of the component”creating the problem

Swap the first component. The swapping is represented as A-R+ and A+R-

If Good assembly becomes Bad assembly, and Bad assembly becomes Good assembly, then Component interchanged is the “Only reason”for the problem

No graph is plotted as in the variable responseList down the Components in the descending order of suspect level



DOE Tool 4

Modified Component Search


M&A Phase DOE 4 –Modified Component Search

Application:• When the problem is on an assembled product & when we

disassemble, some parts will get damaged

• For this tool to be used, some parts should not get damaged and can be reused

• If there is an assembly problem and all the parts are getting damaged during disassembly, use “Product/Process search tool”



M&A Phase: DOE4- Modified Component Search rules checklist

Variable response

After doing Product/Process search, if all the dimensions of the replaced parts are eliminated, then do “Multivari analysis” on the Assembly process


If the conclusion is Assembly process and the replaced parts are not the reasons, then go to Stage # 2

If the conclusion is Assembly process or the replaced parts are the reason for the problem, use “Product/Process search” tool to investigate the replaced parts dimensions.

Totally, we will have 3 data for Good assembly and 3 data for Bad assembly

D/d ratio <1.25, then Assembly Process or the replaced parts are the reason for the problem

Disassemble and Reassemble WOW assembly two times. Replace the parts that are getting damaged with new parts and record the response.

D/d ratio >=1.25 and <3 and there is “Overlap”between the 3 data of Good and 3 data of Bad, then Assembly process “or” the replaced parts are the reasons for the problem

Disassemble and Reassemble BOB assembly two times. Replace the parts that are getting damaged with new parts and record the response.

D/d ratio >=1.25 and <3 and there is “No overlap” between the 3 data of Good and 3 data of Bad, Assembly process and replaced parts are not the reasons. The components that are not getting damaged are the reasons for the problem

When calculating d value, the number of decimal places should be one decimal more than in the data

Note down the data as selected

D/d ratio >=3, Assembly process and replaced parts are not the reasons. The components that are not getting damaged are the reasons for the problem

D = Difference of the Mediand = Average of Ranges

Take one BOB and one WOW assembly




Variable response

Same rules as Paired comparisonSame rules as Paired compairsonSelect 8 BOB and 8 WOW assemblies. Remove the parts pinpointed earlier as per step 2 and then check the suspected dimensions on those parts

Only one line crossing the middle line. Conclusion: One of the component creating the problem

For A+R- data, use the Bad assembly legend“-” indicates Bad assembly and “+” indicates Good assembly


Stage # 3 – Paired comparisonStage # 3 – Paired ComparisonStage # 3 – Paired Comparison

If A is “one of the component” and B is “the only component”, Do paired comparison only on B






No line crosses the middle line: Component not at all creating the problem

For A-R+ data, use the good assembly legendSwap the first component. The swapping is represented as A-R+ and A+R-. Whenever the swapping is done, the replace the damaged parts with a new one.

Both lines crossing the middle line (Average of median line). Conclusion: Only component creating problem

When plotting the data, represent bad assembly data as “dotted line” or “Red color line” and Good assembly data as “Sold line” or “Green color line”

List down the Components in the descending order of suspect level




Attribute response


After Product/Process search, if all the dimensions are eliminated, then the Assembly process has to be investigated through “Observation”

If Assembly process or the replaced parts are the reason for the problem, then do “Product/Process search” for the dimensions of the replaced parts

If Components that are not damaged are the reason for the problem go to Stage #2

No data will be measured and recorded. Just record the status of the assembly as “Good” and “Bad”

Good assembly becomes bad or Bad assembly becomes good, then Assembly process “or” the replaced parts are the reason for the problem

Dissemble and Reassemble Good assembly two times and Bad assembly two times. Replace the parts that are getting damaged

Good assembly remains Good and Bad assembly remains Bad, Assembly Process and the Replaced parts are not the reasons for the problem. Components that are not damaged are the reasons for the problem

No calculations are doneTake one Good and one Bad assembly




Attribute response

Same rules as Paired comparisonSame rules as Paired compairsonSelect 8 Good and 8 Bad assemblies. Remove the parts pinpointed earlier as per step 2 and then check the suspected dimensions on those parts

If Good assembly remains Good and Bad assembly remains Bad, then the Component interchanged is “Not at all” the reason for the problem

“-” indicates Bad assembly and “+” indicates Good assembly



Stage # 3 – Paired ComparisonStage # 3 – Paired Comparison



If we get, A as one of the component, B as one of the component creating the problem, we should not go for C, we have to interchange A&B together


If Good assembly remains Good and Bad assembly becomes Good, then the Component interchanged is “One of the component”creating the problem


If Good assembly becomes Bad and Bad assembly remains Bad, then the Component interchanged is “One of the component”creating the problem

Swap the first component. The swapping is represented as A-R+ and A+R-. During swapping, replace the parts that are getting damaged with new ones.

If Good assembly becomes Bad assembly, and Bad assembly becomes Good assembly, then Component interchanged is the “Only reason”for the problem

No graph is plotted as in the variable responseList down the Components in the descending order of suspect level



DOE Tool 5

Multi vari analysis


M&A Phase DOE 5 – Multi Variable Analysis

Application:• Is used only when response is “variable”.

• Is used only when the problem is generated from a manufacturing process.

• Used to identify what source of variation is the highest in a process

• Response is analyzed in this tool

• All input material parameters are eliminated by using other DOE tools


Types of Variation:

Part to Part Variation:

Variation between consecutive parts from the process is termed as Part to Part variation.SSV’s for Part to Part variation:

•Operator

•Machine( Equipment) - Hardware

•Measurement

•Process Design( design of fixture, toolings, clamping method, specification of process parameter)

specification of process parameter= coolant, feed, speed, etc



Types of Variation:

SSV’s for Time to Time variation:

•Same as reasons for Part to Part variation if the Time to Time variation is less than or equal to Part to Part variation

•If the Time to Time variation is > Part to Part variation, then it is due to Events( power failure, Tool offset, Adjustment, Dressing, break down, etc)

Time to Time:

Variation between time blocks from the process is termed as Time to Time variation.



Types of Variation:

SSV’s for Stream to Stream variation:

•Same as Part to Part variation provided the Stream to stream variation is <= Part to Part variation

•If Stream to Stream variation is >= Part to Part variation, then the reason is due to abnormality in streams.

Stream to Stream:

Variation between streams from the process is termed as Stream to Stream variation.



Identifying Stream

Stream to Stream

ProductStreams

ProcessStreams

• Run out

• Taper

• Journal to Journal

• Pin to Pin

• Spindle to Spindle

• Fixture to Fixture

• Cavity to Cavity

• Line to Line

Checking response at multiple locations on the product

How the process is designed



Types of Stream & No. of Streams

Measuring diameter at three places on both sides

Example

Side A Side B

Top Middle Bottom Top Middle Bottom

In the above example, there are two levels in the tree. Hence there are two types of stream to stream variations

Side to Side is one level and Top-Middle-Bottom is another level

No. Sides = 2

No. of places = 3

Total No. of streams = 6



Measuring diameter at three places on both sides and at each place at two location.

Example

Side A Side B

Top Middle Bottom Top Middle Bottom

In the above example, there are three levels in the tree. Hence there are three types of stream to stream variationsSide to Side is one level, Top-Middle-Bottom is second level and X-Y is third levelNo. Sides = 2No. of places = 3No. of locations = 2Total No. of streams = 12

X Y X Y X Y X Y X Y X Y


Types of Stream & No. of Streams


M&A Phase: DOE5- Multi vari analysis rules checklist

Events should always be “Between time blocks”

Never delete any data for analysis

Ensure that “No known planned/unplanned events”are coming in the 3 consecutive parts within Time block

Check among all which variation is highest.For doing the analysis manually, refer to the next slides for the procedure

Collect continuously 3 parts from each “Process stream”. This is for one time block Eg: if there are 3 process streams, then we have to collect 9 parts. Measure the response and record the data. This time block is “Time 1”

If there are events, coming within the 3 parts, split and create two time blocks, so that events will come between the time blocks

After checking, still if the Part to Part variation is high, then do Variable search or Full factorial for Parameter design

Stop data collection, when Variation is >=80% of tolerance

If P value is >0.05, then check the basic machine condition and rectify for any abnormalities.

Calculate the variation for both the Time -1 and Time -2 data. Check for the same rule as above. If the condition is satisfied, stop data collection, otherwise continue data collection

If the P value is >0.05, then the Part to Part variation is same in all the streams

For doing “Test of Equal Variances”Stat -> ANOVA -> Test of Equal variancesSelect one factor at a time

If the Variation is <80% of tolerance, then collect data for one more time block. This time block is called “Time 2”

For Test of equal variances, Levene’s test, P value <=0.05, then the conclusion is there is a difference in Part to Part variation in the streams

To find out which variation is highestStat -> ANOVA -> Fully Nested ANOVASelect the response, select the parameters in the same order as entered

If the Variation is >=80% of tolerance, then stop the data collection

If Part to Part variation is highest, then do “Test of Equal Variances” in Minitab to find out whether Part to Part variation is equal in all the streams or is different in the streams

Analysis using MinitabCalculate the Range of the entire data (Maximum –Minimum of the entire data). This is the Variation



Example

28131510391113122126Range

1112121514121115184476

13425305141316161620315

125253041520265425334

558163610225811Range

101018268620128108163

55132061014117516212

55101051210106512101

minmaxminmaxminmaxminmaxminmaxminmax

L2L1L2L1L2L1

J3J2J1

Journal1

L1

Max Min

L2

Max Min

Journal1

L1

Max Min

L2

Max Min

Journal1

L1

Max Min

L2

Max Min

Part to Part Variation



Example

Time to Time Variation

4.36Range

15.06Average

1112121514121115184476

13425305141316161620315

125253041520265425334

10.69Average

101018268620128108163

55132061014117516212

55101051210106512101


L2L1L2L1L2L1

AverageJ3J2J1



Example

Stream to Stream Variation ( Max to Min Variation)

54.06.04.3357.3Range

12.007.0021.0025.007.6713.6714.6719.0013.008.0016.3323.67Average

1112121514121115184476

13425305141316161620315

125253041520265425334

05.03.03.670.33.7Range

6.76.713.718.76.39.314.711.07.06.712.015.7Average

101018268620128108163

55132061014117516212

55101051210106512101


L2L1L2L1L2L1

J3J2J1



Example

Stream to Stream Variation ( L1 to L2 Variation)

13.336.29.5Range9.522.810.716.810.520.0Average111212151412111518447613425305141316161620315125253041520265425334

9.55.07.0Range6.716.27.812.86.813.8Average1010182686201281081635513206101411751621255101051210106512101

minmaxminmaxminmaxminmaxminmaxminmaxL2L1L2L1L2L1

J3J2J1



Example

Stream to Stream Variation ( J1- J2- J3 Variation)

2.4216.213.815.3Average

1112121514121115184476

13425305141316161620315

125253041520265425334

1.0811.410.310.3Average

101018268620128108163

55132061014117516212

55101051210106512101


L2L1L2L1L2L1

RangeJ3J2J1



Part to Part Variation

Time to Time Variation

Stream to Stream Variation ( Max to Min Variation)

Stream to Stream Variation ( L1 to L2 Variation)

Stream to Stream Variation ( J1- J2- J3 Variation)

26.00

4.36

7.30

13.33

2.42



DOE Tool 6

Concentration Chart


M&A Phase DOE 6 – Concentration Chart

Application:• Is used when the problem can come anywhere on the product and

we have to find out whether the defect is concentrated in one area or not (eg: blow holes, cracks, porosity, underfill etc..)

• Is used when defect can generated at multiple streams from the process and streams are too high to apply Multi-Vari Analysis.


M&A Phase: DOE 6- Concentration chart rules checklist

Divide the part into different zones depending on the geometry

If in any zone the defect severity % is >=80%, then the defect is concentrated in that zone

Calculate for each zone, the Weighted sum of the severity

Collect 30 bad parts

Note down the severity in each zone

Count on every part, the number of defects generated in each zone

If in all the zones the defect severity is <80%, then the defect is coming randomly

Calculate the % with respect to the total in each zoneScale the severity of defect on a scale of 1-3. 1 –Less severity 2- Medium severity 3 – High severity



DOE Tool 7

B Vs C


M&A and Improvement Phase DOE 7 – B Vs C

Application:• Is used to validate the root cause of the problem identified using

other DOE tools. (DOE Tool 1-6)

• If the cause is validated, then we can calculate how much the improvement has taken place

• Tool is applied only when B & C condition can be created alternately.

• Response is monitored in terms of Big Y

Key Skill of BB : “ Selection of Correct Tool”


M&A Phase: DOE 7- B vs C rules checklist

Always collect data by alternating between the B and C condition

Maximum boundary for the sample size is 12B, 12C.In 12B, 12C, if the amount of improvement cannot be declared, then go back to M&A phase

When calculating Sigma (b), round off the decimal to one decimal more than the data

If the validation is done using batches, decide the batch quantity to get at-least one bad product. Eg: if the historic rejection is 1%, then the batch quantity will be taken as 100 pcs

If (Xb-Xc) is < K* Sigma(b) even at 90% CL, increase the sample size in multiples of 3

When calculating average, round off the decimal place to one decimal more than the data

If the response is attribute, rejection % in each batch will be taken as the data for analysis

For 6B,6C, if the total count is <6, then the cause is not validated and we have to go back to M&A phase

If the response is variable, produce 6 or 3 pieces in B condition and 6 or 3 Pieces in C condition

For 3B, 3C, if there is no overlap, then the root cause is validatedFor 3B, 3C, if there is a overlap, then increase the sample size by 3

For 3B and 3C, check whether is there any overlap in the data or not. If there is no overlap, then the cause is validated

If there is Overlap, then increase the sample size by another 3 and validate as per 6B,6C

If the tool used for finding out the cause or root cause is Paired comparison or Product/Process search and the total count is full count (16 or 12), then the sample size is 3B and 3C

If (Xb – Xc) is >= K * Sigma (b), then the amount of improvement can be declared at 95% CL. If it is less, then get the K value at 90% CL and do the same check

Quantify improvement only when the cause as per the above rule is validated

If the response is variable, measure the actual value of the response as the data for analysis

Quantifying improvementQuantifying ImprovementIf the response is attribute, produce 6 or 3 batches in B condition and 6 or 3 batches in C condition

For 6B,6C if the total count is >=6, then the cause is validated

For 6B, 6C, find out the count using the same rules as “Paired comparison”

In all other situations, the sample size is 6B, 6C



DOE Tool 8

Variable Search


M&A Phase DOE 8 – Variable Search

Application:• Is used when design parameters are >3.

• Can be used for problem solving only when all the variation related SSV’s are eliminated and the cause is confirmed as Process design

• Is also used for existing process optimization to arrive at an optimal setting for cost, productivity and quality

• There are 6 stages in the techniques, numbered as Stage # 0, Stage 1, Stage #2, Stage #3, Stage #4, Stage #5


Six stages in Variable Search:Stage 0: To identify the design parameters and identifying ‘-’ and ‘+’

setting for each parametersStage 1: To find out whether the parameters and the levels identified in

stage 0 are correct or not.Stage 2: To find out which parameters are important and which of the

parameters are not important. To find out whether the contribution of “not important”parameters are zero or not

Stage 3: To validate the significant parameters found in stage2.Stage 4: Do factorial analysis and find out the contribution of each of

the significant parameters and also the contribution of the interactions

Stage 5: Make a mathematical equation based on the contribution of significant parameters and arrive at the optimal setting

M&A Phase DOE 8 – Variable Search


DOE Tool 8

Variable Search

Application: Problem Solving


M&A Phase: DOE 8 – Variable Search rules checklist

Application – Problem solving

Stage # 0 rules

• Two types of design parameters can be selected for Study. One type of design parameter are the parameters taken from the SSV’s and another are the New Design parameters

•Listing of Parameters•Identification of Design parameters from SSV’s

•Check whether the Top or Bottom count is >=3

•If yes, then list that parameter from the SSV as a design parameter

•Identification of New Design parameters

•New design parameters are identified based on the technical knowledge of the problem

•Response is the Problem

•In this application, there will be only one response

•Identification of – and + settings•For Design parameters selected from SSV’s

•Values which have given WOW results are – setting

•Values which have given BOB results are + setting

•For New Design parameters

•Existing setting is the – setting

•+ setting is identified based on technical reasoning and “favorable for Quality” (setting which will reduce the problem)

If the response is attribute, then the data we will take as response is the rejection % of a batch


M&A Phase: DOE 8- Variable Search rules checklist

Application: Problem solving

After two iterations, if we are getting still D/d ratio <1.25, then identify the + setting in Stage # 0 as the setting which will give “more rejection”

If the response is attribute, the rejection % of each batch will be tracked as response

We will have 3 data in – setting and 3 data in + setting

If D/d ratio is >=1.25 and <3, and there is no overlap then the settings identified in Stage # 0 are correct and we can go for Stage # 2

Calculate D/d ratioIf the response is attribute, then we have to produce 3 batches in – setting and 3 batches in + setting

Stage # 1Stage # 1Stage # 1

Produce the 3 pieces or batches by alternating between the – and + setting. Do not produce 3 pieces or batches continuously in – and 3 pieces or batches continuously in + setting

If D/d ratio is <1.25, the settings identified in Stage # 0 are wrong, and we go back to Stage # 0 for changing the + condition or for adding new design parameters

If the response is attribute, the batch quantity will be based on the existing rejection % and the rule is we have to decide the quantity to get at-least one bad. Eg: if the rejection percentage is 2%, then the batch quantity will be 50 pcs.

If D/d ratio is >=3, then the settings identified in stage # 0 are correct and we can go to Stage # 2

D = Difference of Mediand = Average of Ranges

If the response is variable, then we have to produce 3 pieces in – setting and 3 pieces in + setting





If we conclude that the parameter is “NOT AT ALL” creating the problem, then check whether the “Solid or Green line” is within the “Solid or Green limits” and “Dotted or Red line” is within the “Dotted or Red limits”If yes, then the contribution of the parameter is “ZERO”If not, then the contribution of the parameter is “NOT ZERO”

UDL(-) = Median (-) + 1.45*dLDL(-) = Median (-) – 1.45*dDraws these limits as “Dotted or Red line”

If A parameter is concluded as “one of the parameter” and B parameter is concluded as “one of the parameter”, then do not go for C parameter. Do A&B together

If any one line cross the middle line, then that parameter is “ONE OF THE PARAMETER”creating the problem

Calculate 1.45*d, d – average of rangesRound off 1.45*d to the same decimal as data. Always round off to the higher value

Start with the first parameter, which is marked as “A”. Produce one piece or one batch in A-R+ and one piece of one batch in A+R-.


If we conclude that the parameter is the “ONLY PARAMETER” , then check whether the “Solid or Green line” is within the “Dotted or Red limit”and “Dotted or Red line” is within the “Solid or Green limit”If yes, then the contribution of other parameters are “ZERO”If not, then the contribution of other parameters is “Not ZERO”

Draw the + setting line as “Solid line” or “Green color line”Draw the – setting line as “Dotted line” or “Red color line”

For A-R+, use the + setting legend for plotting the data pointFor A+R-, use the – setting legend for plotting the data point

Stop the data collection, once we get the conclusion as “ONLY PARAMETER” creating the problem

If no line crosses the middle line, then that parameter is “NOT AT ALL THE PARAMETER” creating the problem

UDL(+) = Median (+) + 1.45*dLDL(+) = Median (+) – 1.45*dDraw these limits as “Solid or Green line”

If the response is variable, measure the actual value. If the response is attribute, calculate rejection % for the batch

If both the lines cross the middle line (Average of median), then that parameter is the “ONLY PARMETER” creating the problem

Middle line is the Average of MedianList down the parameters in the descending order of suspect level





This analysis can also be done in Minitab

Number of interactions = Number of rows - 1 - number of parameters

Number of rows in the table = 2 ^ n (n – Number of parameters)

Whichever setting is having a “higher average”, put that setting above the contribution

For finding contribution, find out the Average of – setting, Average of + setting and find out the difference

Each row in the table should be read as Combination

If the contribution of A is +2, then when A parameter is changed from + setting to – setting, the response will “DECREASE” by 2

Parameters which are “NOT IMPORTANT” and which are having “ZERO CONTRIBUTION” can be completely ignored from this analysis.

Stage # 4Stage # 4

See the data collected in Stage #1 and Stage # 2, question each data and fit in the corresponding row of the table, provided it fits

Parameters which are “NOT IMPORTANT” and which are “NOT”having “ZERO CONTRIBUTION” should be fixed at a setting favorable for Quality (Could be either – or + setting)

When the parameter is changed from the setting provided above the contribution to the other setting, the response “DECREASES” by the amount calculatedFor eg: if the contribution of A is -2, then when A parameter is changed from – setting to + setting, the response will “DECREASE” by 2

Make the Factorial table only for the Important parameters identified in the previous stage

ConclusionAnalysis




If Y is attribute, then the Boundaries areUpper Boundary = 0Lower Boundary = 0

If Y is variable and Higher is better (Eg: Strength), Calculate the boundary for optimization asUpper boundary = LSL + 2.8 *dLower boundary = LSL + 2.3*d

Coefficients of each parameter is ½ the Contribution

Stage # 5Stage # 5

If Y is variable and Nominal is better (Eg: Diameter), Calculate the Boundary for optimization asUpper boundary = Target + 25% of toleranceLower boundary = Target = 25% of tolerance

If Y is variable and Lower is better (Eg” Runout), Calculate the boundary for optimization asUpper boundary = USL – 2.3*dLower boundary = USL – 2.8*d

Work out multiple settings using ExcelFind out the best setting in terms of Productivity and Cost

Make the Math equation.

ConclusionAnalysis


DOE Tool 8

Variable Search

Application: Process Optimization


M&A Phase: DOE 8 – Variable Search rules checklist

Application – Process Optimization

Stage # 0 rules

•Listing of Parameters•All Parameters which are speed and cost related should be listed down like speed, feed, cycle time, current, gas flow etc..

•If any other parameters which has no effect on cycle time and cost, but has to be changed to take care of the Quality should also be listed. This is purely a technical decision

•Responses are all the Quality parameters that needs to be achieved in that process

•Responses will be Multiple

•Identification of – and + settings•Current setting is the – setting

•+ setting is identified favorable for Cost and Productivity. Eg: if the current setting for Feed is 0.1mm/rev, then in the + setting, feed should be increased. How much we have to increase is an atmospheric decision. General thumb rule, is increase by at-least 15% from the current condition




If D/d ratio is >=1.25 and <3, and there is overlap, then make the “+” setting as “-” setting and identify a new “+” setting. Produce another 3 pieces or batches and again calculate D/d ratio

If the response is attribute, the rejection % of each batch will be tracked as response

We will have 3 data in – setting and 3 data in + setting for every response

If D/d ratio is >=1.25 and <3 and no overlap, then we have to go for Stage # 2

Calculate D/d ratio for every responseIf any one of the response is attribute, then we have to produce 3 batches in – setting and 3 batches in + setting


Produce the 3 pieces or batches by alternating between the – and + setting. Do not produce 3 pieces or batches continuously in – and 3 pieces or batches continuously in + setting

If D/d ratio is <1.25, then make the “+” setting as “-” setting and identify a new “+” setting. Produce another 3 pieces or batches and again calculate D/d ratio.

Do this iteration, till we get difference in any one response

If the response is attribute, batch quantity is 10 pcs

If D/d ratio is >=3, then we have to go for Stage # 2

D = Difference of Mediand = Average of Ranges

If all the responses are variable, then we have to produce 3 pieces in – setting and 3 pieces in + setting





If we conclude that the parameter is “NOT AT ALL IMPORTANT”, then check whether the “Solid or Green line” is within the “Solid or Green limits” and “Dotted or Red line” is within the “Dotted or Red limits”If yes, then the contribution of the parameter is “ZERO”If not, then the contribution of the parameter is “NOT ZERO”

UDL(-) = Median (-) + 1.45*dLDL(-) = Median (-) – 1.45*dDraws these limits as “Dotted or Red line”

If A parameter is concluded as “one of the parameter” and B parameter is concluded as “one of the parameter”, then do not go for C parameter. Do A&B together

If any one line cross the middle line, then that parameter is “ONE OF THE IMPORTANT PARAMETER”

Calculate 1.45*d, d – average of rangesRound off 1.45*d to the same decimal as data. Always round off to the higher value

Start with the first parameter, which is marked as “A”. Produce one piece or one batch in A-R+ and one piece of one batch in A+R-.


If we conclude that the parameter is the “ONLY IMPORTANT PARAMETER” , then check whether the “Solid or Green line” is within the “Dotted or Red limit” and “Dotted or Red line” is within the “Solid or Green limit”If yes, then the contribution of other parameters are “ZERO”If not, then the contribution of other parameters is “Not ZERO”

Draw the + setting line as “Solid line” or “Green color line”Draw the – setting line as “Dotted line” or “Red color line”

For A-R+, use the + setting legend for plotting the data pointFor A+R-, use the – setting legend for plotting the data point

Stop the data collection, once we get the conclusion as “ONLY IMPORTANT PARAMETER”

If no line crosses the middle line, then that parameter is “NOT AT ALL THE PARAMETER”

UDL(+) = Median (+) + 1.45*dLDL(+) = Median (+) – 1.45*dDraw these limits as “Solid or Green line”

If the response is variable, measure the actual value. If the response is attribute, calculate rejection % for the batch

If both the lines cross the middle line (Average of median), then that parameter is the “ONLY IMPORTANT PARMETER”

Middle line is the Average of MedianList down the parameters in the descending order of suspect level





This analysis can also be done in Minitab

Number of interactions = Number of rows - 1 - number of parameters

Number of rows in the table = 2 ^ n (n – Number of parameters)

Whichever setting is having a “higher average”, put that setting above the contribution

For finding contribution, find out the Average of – setting, Average of + setting and find out the difference

Each row in the table should be read as Combination

If the contribution of A is +2, then when A parameter is changed from + setting to – setting, the response will “DECREASE” by 2

Parameters which are “NOT IMPORTANT” and which are having “ZERO CONTRIBUTION” can be completely ignored from this analysis.

Stage # 4Stage # 4

See the data collected in Stage #1 and Stage # 2, question each data and fit in the corresponding row of the table, provided it fits

Parameters which are “NOT IMPORTANT” and which are “NOT”having “ZERO CONTRIBUTION” should be fixed at a setting favorable for Quality (Could be either – or + setting)

When the parameter is changed from the setting provided above the contribution to the other setting, the response “DECREASES” by the amount calculatedFor eg: if the contribution of A is -2, then when A parameter is changed from – setting to + setting, the response will “DECREASE” by 2

Make the Factorial table only for the Important parameters identified in the previous stage

ConclusionAnalysis




If Y is attribute, then the Boundaries areUpper Boundary = 0Lower Boundary = 0

If Y is variable and Higher is better (Eg: Strength), Calculate the boundary for optimization asUpper boundary = LSL + 2.8 *dLower boundary = LSL + 2.3*d

Coefficients of each parameter is ½ the Contribution

Stage # 5Stage # 5

If Y is variable and Nominal is better (Eg: Diameter), Calculate the Boundary for optimization asUpper boundary = Target + 25% of toleranceLower boundary = Target = 25% of tolerance

If Y is variable and Lower is better (Eg” Runout), Calculate the boundary for optimization asUpper boundary = USL – 2.3*dLower boundary = USL – 2.8*d

Work out multiple settings using ExcelFind out the best setting in terms of Productivity and Cost

Make the Math equation.

ConclusionAnalysis


DOE Tool 9

Full Factorial


M&A Phase DOE 9 – Full Factorial

Application:• Is used when design parameters are <=3.

• Is used for Problem solving as well as Existing process optimization.

Note: Difference from Variable Search

In variable search , factorial table is constructed only for significant parameters while in Full Factorial , it is constructed for the all parameters identified.

In this tool, Stage # 2 of Variable search is not done, and the factorial table is made directly and data is collected. Rest of the procedure is same


DOE Tool 10

Variation analysis


Control Phase DOE 10 – Variation Analysis

Application:• Is used to identify the type of controls (monitoring method) that are

required for the action implemented so that the problem does not recur again due to the same root cause.

• Is done only when Product dimensions are the root cause for the problem

• Five options of the control methods are

• No inspection

• Pre-control chart

• X-bar and Range chart with sampling inspection

• X-bar and Range chart with 100% inspection

• Only 100% inspection

• Is used to prove that “Six Sigma ( Estimated part to part variation) ”is 50% of the tolerance if the Big Y is “Variable”.



Steps for Variation Analysis

Identify parameters that requiresVariation analysis(VA)

Calculate no. of Product/processstreams

Decide no. of samples to be Needed for data Collection

Collect data

Do Multi Vari Analysis, if no. ofStreams >1

Calculate part to part(PTP)variation

Check consistency by using RChart,If PTP variation is highest

Estimate PTP variation ( 6σ) byUsing Rbar/d2 formula

Check the normality of data byusing Histogram

Estimate % rejection by usingZ value & Z table

Decide the monitoring methodBy using 6σ, Tolerance & actual

Variation of data

Implement control methodto monitor process

Implement corrective action, ifPTP variation is less than Time toTime/ Stream to Stream variation

1

2

3

4

5

6

7

8

9

10

11

12

13

Start End


Start

List down the parameters based onthat it is1.Variable, 2.Not a functional paramtr3. Rapidly detected, 4. Measured with

Non Destructive Method4. Not generated from batch process

Is part to part variation is high

Identify process/product streams &Make the data table as needed

Decide sampling for . No. of parts within time block- 3 or 5. No. of time blocks needed- Min 25 &

4 hrs

Collect data as per above planCovering 4 hours production

Calculate standard Deviation,σ = R bar / d2 ( R bar can be obtained from R chartor manual calculation & d2 isobtained from Table 1

Is streams are more than one

Do Multi Vari Analysis

Estimate part to part variation,= 6σ

This is done only once

Use range chart and check for part topart consistency i.e. all ranges are

within control limits

Is part to part variationConsistent?

Check for stratification level By using R chart

Are stratification levels> 3?

Check for7 consecutive points In R chart

Are they increasing, decreasing& one side of mean?

Calculate the overall average of data( see normality test for average)

Stop

Is the value of “p”<0.05 ?

Draw the normality test and see the Value of “p”

B

Draw the Histogram for the data

Is the histogramnormal>? BA

Plan for DOE & repeat the steps

EndImplement actions

Yes

Yes

Yes

Yes

Yes Yes

Yes

No

No

No

No

NoNo

No



B

Collect or calculate . Average of data. Sigma( σ ) . Six Sigma ( 6σ ) . USL & LSL. Tolerance

Calculate . ZUSL = ( USL-AVERAGE) / Sigma

. ZLSL.= ( LSL-AVERAGE) / Sigma

Calculate from Z table. % rejection at ZUSL

. % rejection at ZLSL

Calculate Total % Rejection

= % reje. at ZUSL+ % reje at ZLSL

Calculate Cpk. Cpk for USL= ZUSL / 3

. Cpk for LSL= ZLSL / 3

Is 6σ ≤ 75% of Tolerance ?

Is 6σ >75% & ≤ 100% of Tolerance ?

Is actual part to partVariation ≤ 50% of Tolerance ?

Use Pre-Control ChartFor monitoring

Use X bar & R ChartFor monitoring

Use X bar & R ChartWith 100% inspection

For monitoring

Do 100% inspection

Use DOE to reducevariation

End

Is Tolerance known orgiven ? C

Yes

Yes

Yes

Yes

No

No

No

No

2.53462.32652.0594

1.69331.1282

d2Sample size

Table-1

It means 6σ > Tolerance



Is Z ≥ 6 ?

Is Z ≥ 4& < 6 ?

Is Z ≥ 3 & < 4 ?

Use Pre-Control ChartFor monitoring

Use X bar & R ChartFor monitoring

Do 100% inspection

Use DOE to reducevariation

End

Yes

Yes

Yes

No

No

No

C

Use X bar & R ChartWith 100% inspection

For monitoring

A

Rare occurrence. Check the data

Once again

End

Calculation of z value When Tolerance is not given ( Only Min Value is given)

50%206

60%1.6605

75%1.3360ppm4

100%10.273

150%0.674.552

300%0.3331.61

6σ as % of Tolerance

Cpk% Rej.Z value



DOE Tool 11

R&R study


Define Phase DOE 11 – R&R Study

Application:• Is used when there is variation due to method of checking by a

person

• Within person variation is termed as “Repeatability” and is equal to part to part variation. It is also called “Within Person Variation”

• Between person variation is termed as “Reproducibility” and is equal to time to time variation. It is also called “Person to Person Variation ”.

• This study is done only once to find out the variation due to the method of checking

• Variation Analysis DOE tool is used to do R&R study.



Repeatability:• The variation in measurements obtained with one instrument when

used several times by one operator while measuring the identicalcharacteristic on same part. This is within person variation.

Reproducibility:• The variation in the average of measurements obtained with one

instrument when used several times by different operator while measuring the identical characteristic on same part. This is person to person variation.


Start

• Collect Min 5 Pieces,• Do Min 2 Trials for each Person• Select Min 3 person

Collect data as per above & recordin table as per Table-1

Calculate Part to Part variation asPer DOE tool –Multi Vari AnalysisOr use Minitab for R chart and find R bar from R chart

Is no. of ranges>15 ?2.5346

2.32652.05941.69331.1282

d2Sample size

Table-2

74.6860.7745.46T2

74.9961.0245.47T1C

75.4360.8645.33T2

75.4760.8345.39T1B

75.6861.4845.61T2

75.8061.3645.58T1A

Sample 3

Sample 2

Sample 1

TrialMan

Table-1Define Phase DOE 11 – R&R Study

2.542.342.071.711.15152.542.342.071.711.15142.552.342.071.711.15132.552.342.071.711.15122.552.342.081.711.16112.552.342.081.721.16102.552.342.081.721.1692.552.352.081.721.1782.552.352.091.731.1772.562.352.091.731.1862.562.362.11.741.1952.572.372.111.751.2142.582.382.121.771.2332.62.42.151.811.282

2.672.482.241.911.41165432

Group Size (Trials)Ranges

Find out the value of d2 from Table-2 based on no. of rangesAnd no. of trials

Find out the valueof d2 from Table-3

Calculate standard Deviation,σ = R bar / d2

Table-3

A Continued on next slide

No

Yes


A


Check for consistency of ranges

Consistency of within the personvariation is OK

All values of rangesare within UCL & LCL

of run chart?

Consistency of within theperson variation is not OK

End

Estimate within the personVariation at 99%CL asEV= 5.15 σ. This is the Repeatability

Calculate person to personvariation like Time to Time variationdone using Multi Vari Analysis

As there is only one range ( which isthe Time to Time variation) this valueIs equal to R bar

Find out the value of d2from Table-2 as there is only one range

Calculate standard Deviation,σ = R bar / d2

Estimate person to personVariation at 99%CL asAV= 5.15 σ

As AV consist between person Variation also, This is not theReproducibility

Calculate Square of AV & EV

Divide Square of EV by No. ofdata of one person orNo. of Data= No. of Trials x No. of PartsTerm this value as “SEV”

Calculate SAV = Square of AV - SEV

Square Root the value of SAV. The value thus obtained is Reproducibility

BContinued on next slide

No

Yes


B


Calculate the square of SAV

End

Calculate Tolerance of part if not Given asT= 10 x Least count of Instrument

Calculate (TV/ T) x 100

SUM the value square of SAV &Square of EV

Calculate R&R by doing square root of above SUM. This istermed as TV

If above value is ≤30%

Measurement System is not acceptable

Identify the reasons and implementActions and repeat study

No

YesMeasurement System is acceptable.

Measurement system can not beUsed for data collection and analysis

If above value is >30%Calculate (TV/ PV (*)) x 100

Measurement System is acceptable.Measurement system can also be

used for data collection and analysis

(*) PV is taken from the

Variation analysis study as

Sigma * 5.15

Yes

No


DOE Tool 12

Instrument Calibration


Define Phase DOE 12 – Variation due to Instrument

Error = Average of measurement – Value of Master

Measurement Uncertainty: Variation in the error

Types of Measurement Uncertainty:

1. Random Uncertainty

2. System Uncertainty

Linearity: Variation in the error across the range of the instrument


Start

Collect Min 5 reading from instrument


Calculate average of abovereadings

Calculate Error = Actual average – Master Value

Calculate Range R= Max Value – Min Value

As there is only one rangeHence R = R bar

Find out the value of d2 from Table 1 is for one range

Table-1

2.1448

2.1604

2.1788

2.2010

2.2281

2.2622

2.3060

2.3646

2.4469

2.5706

2.7764

3.1825

4.3027

12.706

t values

2.542.342.071.711.15152.542.342.071.711.15142.552.342.071.711.15132.552.342.071.711.15122.552.342.081.711.16112.552.342.081.721.16102.552.342.081.721.1692.552.352.081.721.1782.552.352.091.731.1772.562.352.091.731.1862.562.362.11.741.1952.572.372.111.751.2142.582.382.121.771.2332.62.42.151.811.282

2.672.482.241.911.41165432

Group Size (Trials)Ranges/ Trials

d2 value

Calculate standard Deviation,

σ = R bar / d2

Calculate standard Deviation forAverages as σ x = σ / √ n

Where n= no. of trials

Get the ‘t’ value at 95% CL fromTable 1 based on no. of trials

Estimate Variation at 95%CL asRU = ± ( t x σ ) and is termed asRandom Uncertainty

If System( master) Uncertaintyis also given then termed it asSU

Calculate Total Uncertainty as

TU = ± √Sqr of RU + Sqr of SU

Calculate Upper & Lower LimitAs UL = Error + TU

LL = Error - TU

Check whether zero liesbetween these limits. A Continued on next

slide


If “0” lies between limits

Error is not Zero & Instrument can notbe used

Error is Zero

A

Calculate tolerance T

Calculate (TU/ T)x100

If % < 25%

Uncertainty is acceptable& instrument can be used.

Uncertainty is not acceptable


End

No

No

Yes

Yes

Documents

Tools Application Rules · PDF fileKey skills of BB : Process knowledge, Good observation and correct selection of tools 1 Six Sigma Implementation Tools Application Rules Checklist